A mathematical model of the thermally induced nonlinear propagation of a laser beam in an absorbing fluid medium is developed. The theory includes, identifies, and clearly assesses the relative importance of the different regimes due to conduction, free convection, and/or forced convection cooling. The derived equations of propagation explicitly account for the diffraction effects and permit a straightforward estimate of their relative influence with respect to the thermal distortion. More specifically, similarity parameters or scaling laws are deduced from the governing equations. There is a total of five of these parameters, but it frequently happens in practical applications that the actual number is reduced to only one. Finally, sample numerical results are presented to illustrate some of the implications connected with the proposed model, and the qualitative agreement with published experimental data is very gratifying.
Luc R. Bissonnette, "Thermally Induced Nonlinear Propagation of a Laser Beam in an Absorbing Fluid Medium," Appl. Opt. 12, 719-728 (1973)